Question 73678
Well you sure did pick a hard problem to tackle, I'll see what I can do to help. 
{{{9x^3+9x^2-19x-7=0}}}Start with the given polynomial
{{{9x^3+9x^2-18x-x-6-1=0}}}Rewrite the polynomial in terms that are in common with the rest of the polynomial. For instance, 18 is divisible by 6. These tricks are somewhat difficult since there are no set rules for when or how you use them.
{{{(9x^3+9x^2)+(-18x-6)+(-x-1)=0}}}Start grouping common terms
{{{9x^2(x+1)-6(3x+1)-(x+1)=0}}}Factor out GCF of each grouped term. Notice how we have a common factor of x+1. We can subtract like terms (it's like saying y=x+1 and 9x^2y-y=(9x^2-1)y)
{{{9x^2(x+1)-(x+1)-6(3x+1)=0}}}
{{{(9x^2-1)(x+1)-6(3x+1)=0}}}
Now factor the (9x^2-1) term to get (3x+1)(3x-1) notice the common term of 3x+1. Add these like terms.
{{{(3x+1)(3x-1)(x+1)-6(3x+1)=0}}}
{{{((3x-1)(x+1)-6)(3x+1)=0}}}So if you use synthetic division,  you will find that 3x+1 is a factor and x=-1/3 is a zero. You can use this information to find the other zeros. When you use synthetic division, you will get {{{3x^2+2x-7}}} which is a factor (ie {{{(3x^2+2x-7)(3x+1)=9x^3+9x^2-19x-7}}}
Now use the quadratic formula on 3x^2+2x-7 to find the other zeros
*[invoke quadratic "x", 3, 2, -7 ]
So your zeros are x=-1/3, x=1.23014, and x=-1.89681 
Feel free to ask about any step. Hope this helps.